The known sequence {an} satisfies: 2A1 + 2A2 + +2an-1 + 2An = 2n + 1-2, n ∈ n *. (1) find the general term formula of the sequence {an}; (2) let BN = 2anan + 1, the sum of the first n terms of the sequence {BN} be TN. if there is a real number λ such that λ ≥ TN, try to find the minimum value of the real number λ

(1) When n ≥ 2, ∵ 2A1 + 2A2 + +2an-1+2an=2n+1-22a1+2a2+… +When n = 1, 2A1 = 22-2, the solution is A1 = 1, which also conforms to the above formula. The general formula of {an} sequence is an = n; (2) from (1), we can know that BN = 2anan + 1 = 2n

Seeking indefinite integral ∫ 3 ^ x * e ^ xdx

Using (a ^ x) '= a ^ x · LNA
∫3^x·e^x dx
=∫(3e)^x dx
=1/ln(3e)·(3e)^x+C

Party A and Party B go on at an average speed from AB and meet 70km away from A. the latter two go on, turn back after reaching their destination and meet 90km away from A. ask how many kilometers are there between AB and a

First, we draw a picture and find that a walked 70km at the first meeting, a total distance of a and B walked, and B walked 70 + 90 = 160 (km) at the second meeting, a total of three total distances of a and B. because the speed of the two people is always the same, we can see that the time from the first meeting to the second meeting is twice that of the first meeting, so B walked 160 / 2 = 80 (km) at the first meeting. To sum up, the distance between the two places is 80 + 70 = 150 (km)

What are the physical vectors of senior one

Force F, acceleration a, velocity V, displacement s and so on. If you can't remember them clearly, please list them. Remember that vector scalar with direction and size has no direction

The No.1 bus at the bus station will be sent out every 12 minutes, and the No.2 bus will be sent out every 15 minutes. After the two buses leave at the same time, how many minutes will they leave at the same time?

This is a problem of least common multiple
The least common multiple of 12 15 is 60
60 minutes

If the intersection of the three heights of a triangle is exactly one vertex of the triangle, the shape of the triangle is______ ．

∵ the intersection of the three heights of a triangle is exactly a vertex of the triangle, and the triangle is a right triangle

We know that f (x) = LNX + x2 BX. (1) if the function f (x) is an increasing function in its domain of definition, we find the value range of B; (2) when B = - 1, let g (x) = f (x) - 2x2, we prove that the function g (x) has only one zero point

(1) ∵ f (x) is increasing on (0, + ∞), and ∵ f ′ (x) = 1 x + 2 X-B ≥ 0 is constant for X ∈ (0, + ∞), that is, B ≤ 1 x + 2 x is constant for X ∈ (0, + ∞), only B ≤ (1 x + 2 x) min (x ＞ 0), ∵ x ＞ 0, ∵ 1 x + 2 x ≥ 22, if and only if x = 22, take "=", ∵ B ≤ 22, ∵

1. In the young singer Grand Prix held in a certain city, 11 judges gave a singer a score. If the highest score is removed, the singer's average score is 9.52. If the lowest score is removed, the singer's average score is 9.59. Q: how much is the difference between the highest score and the lowest score?
When Party A completes 1 / 2 of his tasks, the ratio of completed tasks to unfinished tasks is 1:4; when Party A completes all his tasks, Party B still has 1 / 3 of his tasks unfinished. Given that Party B makes 84 parts per hour, how many parts does Party A make per hour?

Question 1: 0.7
Question 2: 126

Y = xsinx, x = 4 parts of π to find the derivative, the specific process, detailed, urgent

y'=sinx +xcosx
x=π /4 y'=√2/2+(π /4)*√2/2=(1+π /4)√2/2

Xiao Gang finished reading a book. On the first day, he read 2 / 15 of the whole book. On the second day, he read 6 more pages than on the first day. At this time, the ratio of the number of pages he had read to the number of remaining pages was 3:7. How many more pages can Xiao Gang read the whole book?

Let the total number of pages be X
Then (2 / 15x * 2 + 6) / x = 3:10
X = 180
So the number of pages to read is: 180 * 7 / 10 = 126 (pages)